Comparison with OMD with truncated linear model To the best of our knowledge, there are actually no regret guarantees with OMD with truncated linear models in the literature ([1]} do not consider the adversarial setting). However, it is quite likely that OMD with truncated models can achieve an implicit regret similar to that reported by [2]} subject to oracle tuning of the learning rates. Our results match this benchmark in the dependency on \({g}_t\)  and \({g}_t^+\)  and improve in the dependency on \(\Vert {u}\Vert \)  since we do not require oracle tuning of the learning rate.
